JavaScript Math atanh()

In this tutorial, you will learn about the JavaScript Math.atanh() method with the help of examples.

The atanh() method computes the hyperbolic arctangent of the specified value and returns it.

Example

// hyperbolic arctangent of 0.75
let number = Math.atanh(0.75);
console.log(number);
 
// Output: 0.9729550745276566

atanh() Syntax

The syntax of the Math.atanh() method is:

Math.atanh(number)

Here, atanh() is a static method. Hence, we are accessing the method using the class name, Math.


atanh() Parameter

The atanh() method takes a single parameter:

  • number - between -1 and 1 whose hyperbolic arctangent is to be calculated

Math.atanh() Return Value

The atanh() method returns:

  • hyperbolic arctangent of the argument number
  • NaN (Not a Number) if the argument is either non-numeric or greater than 1 or less than -1

Example 1: JavaScript Math.atanh() with argument between -1 and 1

// hyperbolic arctangent of 0 let number1 = Math.atanh(0);
console.log(number1);
// hyperbolic arctangent of 0.5 let number2 = Math.atanh(0.5);
console.log(number2); // Output: // 0 // 0.5493061443340548

In the above example,

  • Math.atanh(0) - computes the hyperbolic arctangent of 0
  • Math.atanh(0.5) - computes the hyperbolic arctangent of 0.5

Note: Hyperbolic arctangent i.e, atanh(number) is a unique number 'x' in the range [-1, 1] such that tanh(x) = number.


Example 2: Math.atanh() for Argument not in the Range -1 to 1

// argument greater than 1
let number1 = Math.atanh(2);
console.log(number1);
// argument less than -1
let number2 = Math.atanh(-4);
console.log(number2); // Output: // NaN // NaN

The atanh() method returns NaN because both the arguments 2 and -4 are not in the range -1 and 1.


Example 3: Math.atanh() for Arguments -1 and 1

// atanh() with argument -1 let number1 = Math.atanh(-1);
console.log(number1);
// atanh() with argument 1 let number2 = Math.atanh(1);
console.log(number2); // Output: // -Infinity // Infinity

The atanh() method returns:

  • Infinity - if the argument is 1
  • -Infinity - if the argument is -1

Example 4: Math.atanh() with Non-Numeric Arguments

let string = "Harry";

// atanh() with string argument let value = Math.atanh(string);
console.log(value); // Output: NaN

In the above example, we have tried to calculate the hyperbolic arctangent of the string "Harry". Hence, we get NaN as the output.



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